It's basically the idea that if you give rich people tax cuts, they will use that extra money to invest in the stock market which will grow the economy. It works for a very short period of time (because a lot of rich people do invest in the stock market when they have extra money), but it eventually crashes the whole thing because demand hasn't risen whatsoever. You can't grow the economy when consumers don't have any spending money, and giving more money to the wealthy isn't giving any more money to consumers.

Here's a metaphor: Imagine I want to grow a shoe company, but nobody has any money to buy shoes. If I give more money to the people who own the shoe company, is that going to make the shoe company successful? It might allow it to coast for a bit, but there is still the central problem that nobody has any money to buy shoes. And that lack of demand will eventually crash the shoe company, no matter how much money I give to the owners.

Personally I say we should end the whole game and just build anarcho-communism, but there's a short rundown of it using the language of capitalism

manicatorman: "You can't grow the economy when consumers don't have any spending money,"

This is the central truth that the supply siders ignore. In 2008 we bailed out the banks, because they convinced Congress that they were necessary to the economy. If we had instead bailed out the consumers, especially the homeowners with junk and outright fraudulent mortgages, foreclosures and subsequent layoffs would have been partially averted, and the bankers would have gotten the money eventually anyway, just after it passed through middle class hands.